Youngster David Brooks scored an impressive late winner as 2,317 Blades fans packed into Chesterfield's Proact Stadium.
Chesterfield held a first half lead through Chris O'Grady but Jack O'Connell levelled ahead of Brooks drilling home the winner with five minutes to go.
Blades boss Wilder started with 10 of the 11 that kicked off the game at Malaga. Stevens replaced Lafferty in the left wing back role. There was also a number of Academy players on the bench. Missing out were Hanson (thigh), Evans (hip), Baldock (ankle) and Duffy, who's partner had given birth earlier in the day.
The Blades started brightly, forcing a chance inside four minutes when a corner routine involving Fleck and Carruthers resulted in Freeman's goalbound shot being blocked.
Moore made comfortable saves from Dimaio and Brewster but Chesterfield grabbed the lead just after the half hour. From Wakefield's pass, Brewster held off O'Connell before laying off for O'GRADY to sidefoot home from a central position.
Following the goal, United were on the front foot looking for a leveller but the Spireites headed numerous crosses clear. Late in the half a deep Fleck corner was headed wide at the back post by O'Connell.
The Blades were quickly on the offensive after the interval, with some patient build up around the Chesterfield box. Carruthers cut inside from the right but his shot was deflected wide and then a Coutts run set up a shot for midfield partner Fleck, but goalkeeper Anyon saved.
Chesterfield had their chances, too. O'Grady sliced a volley wide and on 64 minutes Ugwu missed the chance of the season so far. He latched onto Fleck's poor back pass and rounded Moore but with the goal gaping, he fired against a post.
Lavery and Brooks were introduced midway through the half and both had shots blocked, from the latter the ball broke to O'CONNELL, who drilled in United's equaliser from 25 yards - Anyon beaten at his near post.
Boss Wilder made more changes with Thomas, Wright and Lafferty brought into the action as United continued to force back the home side back, twice Brooks went close as the final ten minutes approached.
Two chances from Thomas followed. Following patient build up he curled just over and then a run from the halfway ended with him shooting wide.
The winner, however, was just moments away on 85 minutes and was an impressive goal. BROOKS lifted the ball over Maguire in midfield and following a 30-yard run, he drilled into the bottom corner of Anyon's goal.
There was still time for a Chesterfield chance but McCourt's 30-yarder came back off the crossbar as the Blades made it three wins in three.
Chesterfield: Anyon, Hird, Wiseman, Evatt, O'Grady, Wakefield, Dimaio, Brewster, Donohue, Maguire, Barry.
Unused: Dorel, McGinn, Smith, Reed, Mitchell, McCourt, Brownell, German, Ugwu.
Blades: Moore, Stevens (Lafferty 74), Fleck, O'Connell, Basham, Clarke (Brooks 67), Sharp (Lavery 67), Coutts, Freeman, Stearman (JM Wright 74), Carruthers (Thomas 74).
Unused: Slater, Bennett, Graham, JD Wright, Eastwood.